Over the last years, digitization of various information such as video information and audio information has drastically increased a volume of digital information. To accommodate the increased digital data volume, larger-capacity and higher-density optical disks and optical disk devices have been developed. Further, the advancement of high-density digital information has been associated with a poor quality of reproduced signals from the optical disk. Thus, there is a present need in particular to evaluate a reproduced signal.
A reproduced signal from the optical disk is evaluated, for example, to ensure product quality before the optical disk is shipped, or to adjust various components of the optical disk device to optimize the quality of the reproduced signal.
Conventionally, evaluations of optical disks and optical disk devices have been carried out by measuring jitter or bit error rate (BER). In recent years, this evaluation method has been replaced by the PRML (Partial Response Maximum Likelihood) method, which is a data detection method for realizing high-density recording. An evaluation device suitable for the PRML method is disclosed in Japanese Unexamined Patent Publication No. 21651/1998 (Tokukaihei 10-21651) (published on Jan. 23, 1998).
Referring to FIG. 4 and FIG. 5, the following explains this conventional signal evaluation device which evaluates a recording medium, such as optical disks, or a recording medium driving device, by evaluating a reproduced signal. The signal evaluation device of this conventional example decodes a reproduced signal by Viterbi decoding. Here, the code is (1, 7) RLL with a minimum run length of 1, and PR (1, 2, 1) is used for the PRML method. As indicated by Table 1 below, the state Sk of recorded bit sequence bk at sample point k is S0, S1, S2, or S3.
TABLE 1STATERECORDED BITSkbk-1bkS000S101S211S310
The state changes from one state to another according to the next recording bit. This transition of a state is called branching. Table 2 shows how the state changes according to the recording bit. As noted above, the code used here is (1, 7) RLL with a minimum run length of 1. That is, the minimum run length is restricted to 1, which accounts for the six branches a, b, c, d, e, f.
TABLE 2EXPECTEDRECORDED BITSTATEVALUENo.bk - 2bk - 1bkSk - 1SkYka000S0S0−1.0b100S3S0−0.5c001S0S1−0.5d011S1S20.5e111S2S21.0f110S2S30.5
Table 2 contains expected value Yk, which indicates a reproduced signal level of an ideal waveform which contains no noise, because, in PR (1, 2, 1), the reproduced signal level is determined by the 3-bit recording bit sequence. Here, the reproduced signal level of the ideal waveform has been normalized to have a minimum value of −1 and a maximum value of 1.
Here, the branch metric (Zk−Yk)2 of each branch at sample point k is calculated, where Zk is the reproduced signal level at sample point k, and Yk is the expected value of the reproduced signal level. That is, the branch metric is the square of a difference between a reproduced signal level and its expected value, and therefore indicates a square error of the reproduced signal level with respect to the expected value.
The branch metric is used to select a branch when two branches merge into one state. Branches that are continuous are called a path, and a sequence of selected branches is called a surviving path.
In this instance, when the accumulative value of branch metrics with respect to the surviving path in each state at sample point k-1 is mk-1, the accumulative value of branch metrics at sample point k is given by the sum of mk-1 and the branch metric bmk at sample point k. As described, since the branch metric is indicative of a square error, the accumulative value is the sum of errors. Therefore, the branches that are selected out are those which would give a smaller value of mk-1+bmk.
For example, the branches that enter the state S0 at sample point k are branch a, which changes from S0 to S0, and branch b, which changes from S3 to S0, as Table 2 indicates. When the accumulative values of the branch metrics of branch a and branch b are m0k-1 and m3k-1, respectively, and when their respective branch metrics are bmak and bmbk, then the accumulative values m0k(a) and m0k(b) of branch metric a and branch metric b at sample point k are given by the following equations (1) and (2), respectively.m0k(a)=m0k-1+bmak  (1)m0k(b)=m3k-1+bmak  (2)
The values of m0k(a) and m0k(b) are compared, and the branch which gives the smaller value is selected.
Here, when the correct state at sample point k is S0, and when the correct transition is a, the equationΔmk=m0K(b)−m0k(a)  (3)is calculated, where Δmk is called a differential metric.
When the correct state at sample point k is S0, and when the correct transition is b, the differential metric Δmk becomesΔmk=m0k(a)−m0k(b)  (4).
That is, the accumulative value of the branch metric of the correct transition is subtracted from the accumulative value of the branch metric of the incorrect transition. For the determination of a correct state and a correct transition, a method described in the foregoing publication can be used, which uses a recorded data sequence, or delays a reproduced data sequence when the error rate of the reproduced data sequence is low.
The result of decoding, i.e., the differential metric Δmk, is positive when the selected branch is correct, and is negative when the selected branch is incorrect.
FIG. 4 shows a distribution of differential metrics calculated at each sample point. Assuming that the differential metric distribution can be approximated to a normal distribution, the means is given by μ, and the standard deviation by σ. The probability that the differential metric has a negative value is equal to the bit error rate (BER), because the differential metric becomes negative when there is an error, i.e., when the incorrect branch is selected, as explained above. That is, the BER can be estimated by calculating the following equation (5)
                    BER        =                              1                                                            2                  ⁢                                                                          ⁢                  π                                            ·              σ                                ⁢                                    ∫                              -                ∞                            0                        ⁢                                          ⅇ                                  -                                                                                    (                                                  t                          -                          μ                                                )                                            2                                                              2                      ⁢                                                                                          ⁢                                              σ                        2                                                                                                        ⁢                                                          ⁢                              ⅆ                t                                                                        (        5        )            
In the event where a relative quality of the reproduced signal, not the absolute value of the BER of the optical disk or optical disk device is sought, σ/μ may be used as an index of the reproduced signal quality.
Incidentally, the distribution of differential metrics shown in FIG. 4 has a single peak. However, where the minimum run length is restricted, the distribution of differential metrics would contain a plurality of peaks, as shown in FIG. 5. It is possible in this case to calculate the BER as if the distribution has a single peak, by regarding the peak closest to 0 as the only peak in the distribution and assuming that the distribution of differential metrics is a normal distribution in a domain of differential metrics to the left of μ in FIG. 5. However, unlike the distribution having the real single peak, μ cannot be determined from the calculated mean, and accordingly standard deviation σ cannot be obtained.
In order to solve this problem, the foregoing publication extracts only the sequence which would give the highest probability of producing negative differential metrics, i.e., the sequence which traces a path that forms a distribution with a closest-to-zero peak. With this processing, a distribution with a single peak, as shown in FIG. 4, can be obtained, thereby enabling the mean μ and standard deviation σ to be calculated relatively easily.
However, while a distribution with a single peak can be obtained by extracting only the data sequence which traces a predetermined path, this processing requires a complex device structure. For example, in PR (1, 2, 1), it is required to find four paths of continuous four different states making specific transitions and to extract only the paths which coincide with these paths. This requires four 5-bit comparators.
Further, the number of paths which need to be found becomes different depending on the PR mode. In PR (1, 2, 2), it is required to find sixteen paths of continuous five different states which make specific transitions. This requires sixteen 6-bit comparators.
Thus, the signal quality evaluation device of the foregoing publication requires a large number of comparators to find and extract particular paths, with a result that the device structure becomes complex.
Further, because the extracted paths are different for each PR mode, the comparators cannot be shared in the evaluations in different PR modes. That is, the signal evaluation device is only applicable to the evaluation in a particular PR mode, and it cannot be used for the evaluations in more than one PR mode.
Meanwhile, a jitter, which has been conventionally used as a criterion for evaluating a reproduced signal quality in optical disks has been replaced by the PRML method, which is a data detection method for realizing high-density recording. Under these circumstances, a jitter, which indicates variations on a time axis, is not suitable as a criterion for the evaluation. Further, it is also common to use a bit error rate, which is a result of data detection by the PRML method, to evaluate a reproduced signal quality. However, this method is associated with many drawbacks, such as a large number of sample bits required for the measurement, and susceptibility to defects due to a scratch on the disk, for example.
In light of these backgrounds, there has been proposed an evaluation method of a reproduced signal quality, known as SAM (Sequenced Amplitude Margin) (T. Perkins, A Window-Margin-Like Procedure for Evaluating PRML Channel Performance; IEEE Transactions on Magnetics, Vol. 31, No. 2, 1995, pp. 1109–1114).
The concept of SAM is described below with reference to FIG. 18 through FIG. 20(a) and FIG. 20(b). The following description is based on the case of PRML detection in which a reproduced signal of a bit string which was recorded with the (1, 7) RLL (Run Length Limited) code is detected according to the PR (1, 2, 1) characteristics.
According to the PR (1, 2, 1) characteristics, the reproduced signal waveform of an ideal 1T mark having no distortion or noise has a channel-clock-based sample level ratio of 1:2:1, as shown in FIG. 18. The reproduced signal waveforms of 2T or greater marks are determined by superimposing the reproduced signal waveform of the 1T mark, so that the sample level ratios of the 2T mark, 3T mark, and 4T mark become 1:3:3:1, 1:3:4:3:1, and 1:3:4:4:3:1, respectively.
In this manner, an ideal reproduced signal waveform is assumed for an arbitrary bit string, and five ideal sample levels 0, 1, 2, 3, 4 are set. Here, for simplicity, the sample levels are normalized to have peak amplitude values of +1 and −1, and accordingly the ideal sample levels are −1, −0.5, 0, +0.5, +1.
The PRML decoding is implemented by the Viterbi decoding. Here, the trellis diagram as shown in FIG. 19 is considered to explain the Viterbi decoding. In FIG. 19, S(00), S(01), S(10), S(11) indicate states, and, for example, S(00) means that the preceding bit and the current bit are both 0. The line which connects one state to another is called a branch, and it indicates a state transition. For example, the branch which indicates a transition from S(00) to S(01) can represent a bit string 001.
In FIG. 19, each branch has an identifier a through f, each with an ideal waveform level expected in its state transition. For example, the branch a represents a bit string 000 and has an ideal level −1, and the branch b has a bit string 100 and has an ideal level −0.5. There is no branch from S(01) to S(10) and from S(10) to S(01), reflecting the impossible bit strings 010 and 101 in the (1, 7) RLL code whose run length is limited by d=1.
In the trellis diagram, to consider all combinations of branches which connect one state to another (called “paths”) is to consider all possible bit strings. Thus, the actual reproduced waveform from the magneto-optical recording medium can be compared with the expected ideal waveform of each path to find a path with the closest waveform, i.e., a path with an ideal waveform having the shortest Euclid distance. In this way, the most likely path can be regarded as the correct path.
The following explains the processes of the Viterbi decoding in more detail, with reference to the trellis diagram of FIG. 19. At an arbitrary time, two paths merge into state S(00) and into state S(11), while a single path extends to state S(01) and to S(10). With respect to each set of the two paths which merge into state S(01) and state S(11), the path with an ideal waveform that gives a shorter Euclid distance from the reproduced signal waveform is selected as a surviving path. As a result, four paths remain at an arbitrary time, respectively extending to the four states.
The square of the Euclid distance between the ideal waveform of a path and the reproduced signal waveform is called a path metric. The path metric is determined by calculating the accumulative value of branch metric, which is the square of a difference between the ideal sample level of a branch and the sample level of the reproduced waveform, with respect to all the branches making up the path.
The branch metrics are calculated from the following equations (13) through (16), and the path metrics are calculated from the following equations (17) through (20),Ba[t]=(X[t]+1)2  (13)Bb[t]=Bc[t]=(X[t]+0.5)2  (14)Bd[t]=Be[t]=(X[t]−0.5)2  (15)Bf[t]=(X[t]−1)2  (16)M(00)[t]=Min{M(00)[t−1]+Ba[t], M(10)[t−1]+Bb[t]}(Min{m,n}=m(if m≦n); n(if m>n))  (17)M(01)[t]=M(00)[t−1]+Bc[t]  (18)M(10)[t]=M(11)[t−1]+Bd[t]  (19)M(11)[t]=Min{M(01)[t−1]+Be[t], M(11)[t−1]+Bf[t]}(Min{m,n}=m(if m≦n); n(if m>n))  (20)where X[t] is the sample level of the reproduced signal waveform at time t, Ba[t], Bb[t], Bc[t], Bd[t], Be[t], Bf[t] are the branch metrics of the branches a, b, c, d, e, f, respectively, at time t, and M(00)[t], M(01)[t], M(10)[t], M(11)[t] are the path metrics of the surviving paths of the states S(00), S(01), S(10), and S(11), respectively, at time t. The process of selecting a smaller path metric of M(00)[t] and M(11)[t] is the selection of a surviving path.
By repeating the process of selecting a surviving path in response to input of a sample value of the reproduced signal waveform, the paths with larger path metrics are successively eliminated before the paths eventually converge into a single path. This path is regarded and used as the correct path to correctly reproduce the original data bit string.
Given this condition of Viterbi decoding, in order for the paths to converge into a single correct path, it is required that the path metric of the correct path be smaller than the path metric of the incorrect path every time a surviving path is selected. This condition is given by the following expressions (21) through (24), according to different correct bit strings.
When the correct bit string is . . . 000,ΔM=(M(01)[t−1]+Bb[t])−(M(00)[t−1]+Ba[t])>0  (21).
When the correct bit string is . . . 100,ΔM=(M(00)[t−1]+Ba[t])−(M(01)[t−1]+Bb[t])>0  (22).
When the correct bit string is . . . 011,ΔM=(M(11)[t−1]+Bf[t])−(M(01)[t−1]+Be[t])>0  (23).
When the correct bit string is . . . 111,ΔM=(M(01)[t−1]+Be[t])−(M(11)[t−1]+Bf[t])>0  (24).
Also, when the correct bit string is . . . 001 or . . . 110, ΔM is always greater than 0 because the selection of a surviving path never fails in this case.
In the foregoing expressions (21) through (24), ΔM is a difference of path metrics of two paths being chosen, and it is called a SAM. To avoid error, it is required that SAM>0. Further, the larger the SAM value, the smaller the probability of an error.
In order to evaluate reliability of the system using the SAM value, a distribution of SAM values calculated at each time must be evaluated in its entirety. The foregoing publication Tokukaihei 10-21651 proposes a method of testing reliability of a reproducing device, using the standard deviation of a frequency distribution of SAM values for the evaluation.
FIG. 20(a) is a graph of a frequency distribution of actual SAM values which were determined from a reproduced signal of a (1, 7) RLL code pattern recorded in a magneto-optical disk. As can be seen from the graph, the SAM distribution has two peaks. This is due to the fact that the Euclid distance between a correct path and an incorrect path becomes different depending on the bit pattern when obtaining SAM values for the entire reproduced signal.
Therefore, as shown in FIG. 20(b), the SAM distribution of a noise-free ideal reproduced signal which was obtained from the (1, 7) RLL code string has a plurality of discrete ideal values 1.5, 2.5, 3.5, 4.5, 5, 6, 7, 8, 9. The ideal values have different frequencies because, in addition to the different numbers of bit patterns for each ideal value, the occurrence of each bit pattern is different in the (1, 7) RLL code string. The actual reproduced signal has various kinds of noise and the ideal values are varied. The result is the distribution pattern with a combination of different distributions, as FIG. 20(a) illustrates.
The SAM distribution, with these characteristics, is very different from normal distributions. Therefore, simply finding a standard deviation from the SAM distribution only gives a little correlation with the bit error rate.
For this reason, the foregoing Tokukaihei 10-21651 creates a SAM distribution by selecting only the bit patterns with the SAM ideal value of 1.5, which have a high probability producing SAM values less than 0 by the influence of a noise, so as to determine a standard deviation with respect to this SAM distribution. This essentially requires a sequence of monitoring patterns of a plurality of data bits resulting from the PRML decoding, and determining SAM values only when the patterns are specific patterns. The drawback of such a sequence is a complex circuit structure. Further, the load on the circuit is large because in order to determine the standard deviation the circuit must calculate the square error of each SAM value and the SAM mean value.
The inventors of the present invention have proposed a method of testing reliability of a reproducing device by first determining relative frequencies according to two different thresholds in a frequency distribution of SAM values and then calculating the bit error rate. Note that, this testing method for a reproducing device is referred to herein only for the purpose of explanation, and it does not constitute known art or prior art of the present invention.
The method of testing reliability of a reproducing device is described below. As described above with reference to FIG. 20(a) and FIG. 20(b), the frequency distribution of SAM values has a distribution pattern with a combination of different distributions because a plurality of SAM ideal values are found with variations by the influence of a noise. Each distribution can be approximated to a normal distribution if the noise is a white noise or close to a white noise. Therefore, a portion of the SAM distribution smaller than the minimum SAM ideal value 1.5 can be nearly approximated to a normal distribution with the mode μ close to 1.5. Here, the standard deviation σ, which indicates a variance of the approximated normal distribution, corresponds one to one to the bit error rate, which relationship is represented by the following equation (34)
                    BER        =                  K          ×                      1                                                            2                  ⁢                                                                          ⁢                  π                                            ⁢              σ                                ⁢                                    ∫                              -                ∞                            0                        ⁢                          exp              ⁢                                                          ⁢                              {                                                                            -                                                                        (                                                      x                            -                            μ                                                    )                                                2                                                              /                    2                                    ⁢                                      σ                    2                                                  }                            ⁢                              ⅆ                x                                                                        (        34        )            
FIG. 28 shows a graph of a frequency distribution of actual SAM values measured from an actual optical disk reproducing device (shown in solid line), superimposed on a normal distribution with the standard deviation σ corresponding to the bit error rate (shown in dotted line).
The last part on the right-hand-side of equation (34) is known in statistics as a distribution function which is determined by integrating a probability density function of a normal distribution, and it indicates a relative frequency in a domain not more than 0 in a normal distribution with mode μ and standard deviation σ. Further, since the error bit in principle occurs when SAM<0, it can be said that the bit error rate BER is equal to a proportion of the domain not more than 0 with respect to all frequencies of the frequency distribution of SAM values. Therefore, the relative frequency in the domain not more than 0 in the normal distribution, multiplied by constant K of modulus transformation, coincides with the bit error rate. More specifically, constant K is obtained fromK=n/Nwhere N is the total frequencies of the frequency distribution of SAM values, and n is the number of patterns which give the smallest SAM ideal value, i.e., the SAM ideal value of 1.5 (a distribution which is created only with the SAM values of such patterns is approximated to a normal distribution with the mode of about 1.5).
With respect to the frequency distribution of SAM values, relative frequencies R1′ and R2′ of domains at or below predetermined threshold values SL1 and SL2, respectively, are measured to give equations (35) and (36) below. These simultaneous equations can be solved for standard deviation σ and mode μ.
                              R1          ′                =                  K          ×                                    ∫                              -                ∞                            SL1                        ⁢                                                            exp                  ⁢                                                                          ⁢                                      {                                                                                            -                                                                                    (                                                              x                                -                                μ                                                            )                                                        2                                                                          /                        2                                            ⁢                                              σ                        2                                                              }                                                                                                              2                      ⁢                                                                                          ⁢                      π                                                        ⁢                  σ                                            ⁢                              ⅆ                x                                                                        (        35        )                                          R2          ′                =                  K          ×                                    ∫                              -                ∞                            SL2                        ⁢                                                            exp                  ⁢                                                                          ⁢                                      {                                                                                            -                                                                                    (                                                              x                                -                                μ                                                            )                                                        2                                                                          /                        2                                            ⁢                                              σ                        2                                                              }                                                                                                              2                      ⁢                                                                                          ⁢                      π                                                        ⁢                  σ                                            ⁢                              ⅆ                x                                                                        (        36        )            
The bit error rate BER can be calculated from equation (34) with the substituted values of standard deviation σ and mode μ obtained from equations (35) and (36).
The calculations of error rate from the relative frequencies of the frequency distribution of SAM values based on two different thresholds thus require solving very complex equations (35) and (36), whose results must then be used to solve equation (34). This is one problem of the foregoing signal evaluation device, because the operation of such calculations takes a notoriously long time when it is run on a microcomputer with software.